Method and Receiver For Jointly Decoding Received Communication Signals Using Maximum Likelihood Detection

ABSTRACT

The present invention relates to a method in a receiver for decoding at least two received communication signals, wherein the communication signals are modulated, pre-coded by a discrete Fourier transform and transmitted by means of single-carrier frequency division multiple access scheme (SC-FDMA). The method comprises the steps of: performing an antenna combining and equalization on a signal observed at the receiver; performing inverse discrete Fourier transform on a model of the observed signal; whitening a time domain model of the observed signal; and jointly detecting the received at least two communication signals by performing soft value calculations based on maximum likelihood detection of a whitened time domain model using a whitened time domain channel estimate.

TECHNICAL FIELD OF THE INVENTION

The present invention relates generally to the field of wirelesstelecommunications and, in particular, to methods and means for decodingreceived communication signals.

BACKGROUND OF THE INVENTION

LTE (Long-term evolution) is a project within the 3GPP (3rd GenerationPartnership Project) with an aim to improve the UMTS (Universal MobileTelecommunications System) mobile phone standard for coping with futuretechnology evolutions. The LTE comprises developing a new air interfacestandard, and the downlink (base station to user equipment) will bebased on OFDMA (orthogonal frequency division multiple access). For theuplink (user equipment to base station), SC-FDMA (single carrierfrequency division multiple access) is an attractive choice as SC-FDMAhas a lower peak-to-average power ratio than OFDM. The lowerpeak-to-average power ratio entails improved transmitter powerefficiency for the battery-operated user equipment, which is animportant design consideration.

In any wireless communication system, a transmitted signal is distorteddue to dynamic properties of a radio channel through which it istransmitted. In order to compensate for the dynamic properties of theradio channel, different methods are available for combatinginterference. An ideal compensation would completely cancel the effectsof the radio channel and the resulting equalized channel would becompletely frequency flat. However, such a scheme would in most caseslead to unwanted noise amplification limiting the performance.Equalization schemes must therefore provide a trade-off between noiseamplification and making the equalized channel frequency-flat.

For the transmitted data to be recovered at the receiver it is importantthat the interference is suppressed. Besides the mentioned powerconsumption aspect of the user equipment, there is also a desire torestrict the size and costs of the user equipment in order for it to beattractive. The desire to reduce size, cost and power consumption isvalid also for receivers in the base station. The space for and costs ofprocessing circuitry should therefore be kept at a minimum. Thecomplexity of the methods used for combating the interference competeswith a desire to cancel the interference to as large extent as possible.The designer thus stands before the choice of using interferencecombating algorithms having less than optimal performance and designinga rather complex and consequently expensive receiver. In short, there isa trade-off between complexity of receiver and performance in terms ofaccuracy.

A particular example of this trade-off is the choice of decoding schemeto be used in the receiver. An advanced detection scheme is the maximumlikelihood detection (MLD), but it has a computational complexity thatis exponential with the number of modulation symbols. Efforts have beenmade to reduce the computational complexity to acceptable levels, anefficient implementation of MLD being, for example, sphere decoding.

In view of the above, it would be desirable to provide simplified andyet effective interference cancellation methods, and in particular a MLDhaving even further reduced complexity than the hitherto known methods.

SUMMARY OF THE INVENTION

It is a general object of the invention to provide a method and receiverfor decoding received communication signals having a balanced trade-offbetween the complexity of the receiver and the performance.

It is a particular object of the present invention to provide animproved method and receiver for decoding a received communicationsignal, the method having reduced complexity and thus enabling thedesign of a receiver having reduced circuitry and thus cost.

It is another object of the present invention to provide a method andreceiver for decoding a received communication signal wherein anequalized and frequency flat channel is provided, and wherein alsospatially coloured noise is suppressed.

These objects, among others, are achieved by methods and receivers asclaimed in the appended claims.

In accordance with the invention, a method in a receiver is provided fordecoding at least two received communication signals. The communicationsignals are being modulated, pre-coded by a discrete Fourier transformand transmitted by means of single-carrier frequency division multipleaccess scheme (SC-FDMA). The method comprises a first step of performingan antenna combining and equalization on a signal Y(m) observed at thereceiver based on a weighting matrix W(m). Thereby a model of observedsignal {circumflex over (X)}(m) and a frequency domain channel estimate{tilde over (H)}(m) are provided. The method further comprises a step ofperforming inverse discrete Fourier transform on the model of observedsignal {circumflex over (X)}(m), thereby providing a time domain model{tilde over (S)}(n) of the observed signal {circumflex over (X)}(m), andperforming an inverse discrete Fourier transform of the frequency domainchannel estimate {tilde over (H)}(m), thereby providing a time domainchannel estimate {tilde over (G)}(p) with length P wherein p=0, 1, . . ., P−1. The method comprises the further step of whitening the timedomain model {tilde over (S)}(n) of the observed signal {circumflex over(X)}(m), thereby providing a whitened time domain model Ŝ(n) of the timedomain model {tilde over (S)}(n) and a whitened time domain channelestimate Ĝ(p) for p=0, 1, . . . , P−1. The method comprises a last stepof jointly detecting the received at least two communication signals byperforming soft value calculations based on maximum likelihood detectionof the whitened time domain model Ŝ(n), using the whitened time domainchannel estimate Ĝ(p) for p=0, 1, . . . , P−1, whereby the receivedcommunication signals are decoded. By means of the invention, a reducedcomplexity of joint detection of communication signals is enabled at areceiver. The error probability is minimized for the case that theoutput of the equalization step is partially available, i.e. dividedinto several smaller parts and each part taken as input to the step ofjoint detection. The feature of whitening the signal, providing aspatially whitened signal, enables the suppression of interference thatis spatially coloured.

In accordance with a variation of the invention, the step of whiteningis performed before the step of joint detection. By performing thewhitening separately before the joint detection, unlike in the prior artwherein such calculations are part of the joint detection, the totalamount of calculations is greatly reduced.

In accordance with another variation of the invention, the step ofjointly detecting comprises a single tap channel model, P=1. Theinventive method is thus applicable to both single-tap channel models aswell as multi-tap channel models, whereby a flexible method is providedeasily adaptable to different applications. By means of the invention,flexibility is provided regarding the trade-off between complexity ofreceiver and performance thereof. The definition of the input to thejoint detection step can be performed flexibly, for example applying thejoint detection to a part of a SC-FDMA symbol or for two consecutivesymbols. The more consecutive symbols that are included, the better theperformance becomes, but at the cost of computational increase.

In accordance with yet another variation of the invention, the methodcomprises, prior to the step of jointly detecting, a step of performingQR factorization of the time domain channel matrix estimate Ĝ, providinga QR factorized signal model Ŝ_(QR)(n) and a time domain channel matrixestimate after QR factorization Ĝ_(QR). The step of jointly detectingthen comprises detecting the QR factorized signal model Ŝ_(QR)(n) by:calculating soft values for bit number i and user k providing two setsof all possible transmitted symbols S_(1,k,i), S_(0,k,i), for whichtransmitted bit is “1” and “0”, respectively; selecting which of the twosets of all possible transmitted symbols S_(1,k,i), S_(0,k,i) toevaluate; and evaluating the selected possible transmitted symbols. Byperforming a QR-factorization, the amount of calculations is reducedeven further, since the channel matrix Ĝ_(QR) is upper triangular.Thereby the use of M-algorithm is enabled.

In accordance with still another variation of the invention, using theM-algorithm, the step of evaluating comprises the steps of: definingmaximum likelihood detection residuals as E(n)=Ŝ_(QR)(n)−Ĝ_(QR)S(n),where E(n)=[e₀(n) . . . e_(K−2)(n) e_(K−1)(n)]^(T),Ŝ_(QR)(n)=[ŝ_(QR,0)(n) . . . ŝ_(QR,K−2) ŝ_(QR,K−1)(n)]^(T) andS(n)=[s₀(n) . . . s_(K−2)(n) s_(K−1)(n)]^(T), whereby residuale_(K−1)(n) only depends on observation symbol ŝ_(QR,K−1)(n) and onsymbol hypothesis s_(K−1)(n),

-   -   (i) calculating, for the last row of the definition, metric        values equal to the absolute square of maximum likelihood        detection residuals for all possible candidates of s_(K−1)(n),    -   (ii) determining M candidates of s_(K−1)(n), providing M        surviving candidates,    -   (iii) repeating steps (i) and (ii) for one additional value of        the observation signal ŝ_(QR,K−2)(n),    -   (iv) calculating, for the M surviving candidates, all possible        transmitted candidates of s_(K−2)(n), and    -   (v) repeating steps (iii) and (iv) for all observation signals.        The use of the M-algorithm greatly reduces the amount of        calculations required for determining, with high probability        which codeword that was most likely to have been sent. The        number of iterations can be held to a minimum.

In accordance with yet another variation of the invention, the step ofjointly detecting comprises soft value calculations performed by meansof Log Likelihood Ratio with squared Euclidian distances or LogLikelihood Ratio based on Euclidian distances. The method is flexible inthat different methods can be utilized for the soft value calculations.

In accordance with yet another variation of the invention, the step ofwhitening comprises: estimating a residual noise-plus-interferencecovariance matrix R_(η) _(k) ; performing Cholesky decomposition of theresidual noise-plus-interference covariance matrix R_(η) _(k) =LL*thereby providing a lower triangular matrix L; whitening the signal timedomain model {tilde over (S)}(n) by multiplying the signal time domainmodel {tilde over (S)}(n) with L*, thereby providing a whitened timedomain model Ŝ(n); and whitening the time domain channel matrix estimate{tilde over (G)} by multiplying the time domain channel estimate {tildeover (G)} with L, thereby providing a whitened time domain channelestimate Ĝ. A method that is easily implemented in e.g. software isthereby provided.

In accordance with still another variation of the invention, the step ofwhitening comprises scaling the received signal, where only the diagonalelements of R_(η) _(k) are used such that the scaling is done with(Diag{R_(η) _(k) })^(−1/2). This embodiment reduces the number ofcalculations required even further, but at the expense of loosing someperformance in terms of accuracy. Again, the method is flexible in thatthe balance between complexity of receiver and performance thereof canbe adapted to suit the particular application at hand.

In accordance with yet another variation of the invention, the step ofscaling comprises estimating a residual noise covariance matrix {tildeover (L)} by a sum of Λ_(N) and Λ_(ISI), wherein Λ_(N) is the noisecovariance matrix of the white noise matrix N_({tilde over (S)})(n) andΛ_(ISI) is inter-symbol interference covariance matrix, and scaling thesignal time domain model {tilde over (S)}(n) by multiplying the signaltime domain model {tilde over (S)}(n) with (Diag{{tilde over(L)}})^(−1/2), providing a scaled time domain model Ŝ(n), and scalingthe time domain channel matrix estimate {tilde over (G)} by multiplyingthe time domain channel estimate {tilde over (G)} with (Diag{{tilde over(L)}})^(−1/2), providing a scaled time domain channel estimate Ĝ. Again,a method that is easily implemented in software and/or hardware is thusprovided.

In accordance with other variation of the invention, the antennacombining comprises performing a linear minimum mean square error,and/or the weighting matrix W(m) is chosen so as to minimize a meansquare error. Well-known and reliable approaches for antenna combiningcan thus be used.

The invention is also related to a receiver comprising means forimplementing the above method, whereby advantages corresponding to theabove-mentioned are achieved.

Further features and advantages thereof will become clear upon readingthe following detailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates one sub-frame for uplink LTE.

FIG. 2 illustrates transmitters for K user equipments, each having oneantenna.

FIG. 3 illustrates the receiver structure for a receiver in accordancewith the present invention.

FIG. 4 illustrates an overview over channel estimator and demodulator.

FIGS. 5 a-5 c illustrates mapping between symbols and bits.

FIG. 6 illustrates an example of QRM-MLD.

FIG. 7 illustrates a flowchart over steps of a method in accordance withthe present invention.

FIG. 8 illustrates a base station and user equipment of a wirelesscommunication network wherein the present invention may be applied.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Only parts of a telecommunication system necessary for the understandingof the present invention are described. For clarity, descriptions ofwell-known devices are thus omitted.

As mentioned in the introductory part, the uplink for LTE is based onSC-FDMA, sometimes also denoted DFTS-OFDM (Discrete Fourier TransformSpread-OFDM) since SC-FDMA can be regarded as a DFT spread OFDM. FIG. 1illustrates one sub-frame 1 for uplink LTE. In the LTE uplink, severalSC-FDMA symbols 2 ₁, . . . , 2 _(i), . . . , 2 _(n) form the sub-frame1. In particular, the sub-frame comprises 12 SC-FDMA symbols 2 ₁, . . ., 2 _(i), . . . , 2 _(n) with user data (UD) and a respective cyclicprefix (CP), n in the illustrated case being equal to 12. The sub-frame1 further comprises two symbols 3 ₁, 3 ₂ with reference signals (RS),for enabling the establishment of channel parameters, the referencesignals sometimes also denoted pilot signals or training signals. Thepresent invention is mainly concerned with such SC-FDMA uplinks.

The present invention will be thoroughly described first with referenceto a special case, after which the generalized inventive concept will bedescribed.

FIG. 2 illustrates a schematic overview of the different steps performedin a transmitter part 5 ₀, . . . , 5 _(k), . . . , 5 _(K−1) of a userequipment in accordance with the invention. In particular, thetransmitter part 5 ₀, . . . , 5 _(k), . . . , 5 _(K−1) comprises means 6for performing a discrete Fourier transform (DFT), means 7 forperforming sub-carrier mapping, means 8 for performing inverse fastFourier transform (IFFT), and means 9 for performing a radiotransmission, described briefly in the following. Such means maycomprise means conventionally used in signal processing, e.g.electronics implementing filters, and/or software etc.

In each SC-FDMA symbol, each user equipment transmits N_(c) symbols,which are demodulated, for example by means of quadrature phase shiftkeying (QPSK) or quadrature amplitude modulation (QAM), e.g. 16 QAM or64 QAM. The SC-FDMA symbol for user equipment k is denoted by S_(k)(n)and can be expressed as:

S _(k) =[s _(k)(0) s _(k)(1) . . . s _(k)(N _(c)−1)]  (1)

These symbols are fed to the DFT, forming transmitted symbols:

$\begin{matrix}{{x_{k}(m)} = {\frac{1}{\sqrt{N_{c}}}{\sum\limits_{n = 0}^{N_{c} - 1}\; {{s_{k}(n)}^{{- j}\frac{2\; \pi \; n\; m}{N_{c}}}}}}} & (2)\end{matrix}$

for frequency index m, 0≦m≦N_(c)−1. Each user is allocated a frequencyinterval, in which it is scheduled for transmission. A scheduler placedin the base station decides this allocation. An allocation of the N_(c)symbols x_(k)(m) to N_(c) sub-carriers in the scheduled frequencyinterval is done in the sub-carrier mapping. Finally, the signals areprocessed in the IFFT, fed to a radio signal processing and sent on theair interface by an antenna.

Although only one transmitter antenna 10 is illustrated for eachtransmitter part 5 ₀, . . . , 5 ₁, . . . , 5 _(K−1), it is noted thatthe present invention can be extended to the case of several transmitantennas for each user equipment.

FIG. 3 illustrates a receiver structure in accordance with theinvention, the receiver 11 being placed e.g. in a base station. Thesignals are received by N_(r) antennas, they are filtered in a radioreceiver part 12, transformed to the frequency domain in an FFT means 13and fed to a sub-carrier extraction means 14. The sub-carrier extractionmeans 14 uses the same sub-carriers as in the transmitter part 5 ₀, . .. , 5 _(k), . . . , 5 _(K−1), as given by a scheduler 15.

In the present application, the sub-carrier mapping, IFFT, transmitterradio, transmitter antennas, air interface channel, receiver antennas,receiver radio FFT and sub-carrier mapping is modelled by a channelmatrix H(m), performed by channel estimator means 16, for frequencyindex m such that the observation signals Y(m), i.e. signals as observedin the receiver 11, equals

$\begin{matrix}{\mspace{79mu} {{{Y(m)} = {{{H(m)}{X(m)}} + {{N(m)}\mspace{14mu} {or}}}}{\underset{\underset{Y{(m)}}{}}{\begin{bmatrix}y_{0} \\y_{1} \\\vdots \\y_{N_{r} - 1}\end{bmatrix}} = {{\underset{\underset{H{(m)}}{}}{\begin{bmatrix}{h_{0,0}(m)} & {h_{0,1}(m)} & {\; \ldots} & {h_{0,{K - 1}}(m)} \\{h_{1,0}(m)} & {h_{1,1}(m)} & \; & \; \\\vdots & \; & \ddots & \; \\{h_{{N_{r} - 1},0}(m)} & \; & \; & {h_{{N_{r} - 1},{K - 1}}(m)}\end{bmatrix}}\underset{\underset{X{(m)}}{}}{\begin{bmatrix}{x_{0}(m)} \\{x_{1}(m)} \\\vdots \\{x_{K - 1}(m)}\end{bmatrix}}} + \underset{\underset{N{(m)}}{}}{\begin{bmatrix}{n_{0}(m)} \\{n_{1}(m)} \\\vdots \\{n_{N_{r} - 1}(m)}\end{bmatrix}}}}}} & (3)\end{matrix}$

In the above expression for observation signals, additive noise N(m) isadded, modelled as Gaussian noise with covariance matrix Λ:

$\begin{matrix}{\Lambda = \begin{bmatrix}\lambda_{0,0} & \lambda_{0,1} & \ldots & \lambda_{0,{N_{r} - 1}} \\\lambda_{1,0} & \lambda_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\\lambda_{{N_{r} - 1},0} & \; & \; & \lambda_{{N_{r} - 1},{N_{r} - 1}}\end{bmatrix}} & (4)\end{matrix}$

The demodulator 17 of the receiver 11 illustrated in FIG. 3 is describedin more detail with reference to FIG. 4.

FIG. 4 thus illustrates the demodulator 17, and in particular comprisingmeans 18 for performing MMSE (minimum mean square error) equalization,means 19 for performing IDFT (inverse discrete Fourier transform), means20 for performing scaling, means 21 for performing QR factorization andmeans 22 for performing joint detection with soft value calculations,all of which will be described in more detail in the following. Observedsignals and residual noise models between the functional blocks are alsoindicated in the figure.

As illustrated in FIG. 4, a channel estimation algorithm provides both achannel estimate

$\begin{matrix}{{\hat{H}(m)} = \begin{bmatrix}{{\hat{h}}_{0,0}(m)} & {{\hat{h}}_{0,1}(m)} & \; & {{\hat{h}}_{0,{K - 1}}(m)} \\{{\hat{h}}_{1,0}(m)} & {{\hat{h}}_{1,1}(m)} & \; & \; \\\vdots & \; & \ddots & \; \\{{\hat{h}}_{{N_{r} - 1},0}(m)} & \; & \ldots & {{\hat{h}}_{{N_{r} - 1},{K - 1}}(m)}\end{bmatrix}} & (5)\end{matrix}$

for frequency index m=0, . . . , N_(c)−1 and a noise covariance matrixestimate

$\begin{matrix}{\hat{\Lambda} = \begin{bmatrix}{\hat{\lambda}}_{0,0} & {\hat{\lambda}}_{0,1} & \ldots & {\hat{\lambda}}_{0,{N_{r} - 1}} \\{\hat{\lambda}}_{1,0} & {\hat{\lambda}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\hat{\lambda}}_{{N_{r} - 1},0} & \; & \; & {\hat{\lambda}}_{{N_{r} - 1},{N_{r} - 1}}\end{bmatrix}} & (6)\end{matrix}$

In FIG. 4, the demodulator 17 is thus described by MMSE equalization,IDFT, scaling, QR factorization and joint detection with soft valuecalculations.

MMSE Equalization

In the present application a linear MMSE antenna combination andequalization is used. It is however noted that other linear equalizationschemes could be used, for example zero forcing. The observation signalsY(m) are multiplied with a frequency dependent weighting matrix W(m)such that

{circumflex over (X)}(m)=W*(m)Y(m)  (7)

where ( )* denotes conjugate and transpose. {circumflex over (X)}(m) isthe MMSE combined observation signal, in the following denoted model ofobserved signal. The weighting matrix W(m) is selected such that theMean Square Error (MSE)

C(m)=E{(X(m)−{circumflex over (X)}(m))*(X(m)−{circumflex over(X)}(m)))}  (8)

is minimized, as is known within the art. The weighting matrix W(m) thusequals

$\begin{matrix}{{W(m)} = {\left( \underset{\underset{\overset{\sim}{\Lambda}{(m)}}{}}{\hat{\Lambda} + {{\hat{H}(m)}{{\hat{H}}^{*}(m)}}} \right)^{- 1}{\hat{H}(m)}}} & (9)\end{matrix}$

wherein {tilde over (Λ)}(m) is a noise and channel covariance matrix ofsize N_(r)×N_(r). This noise and channel covariance matrix needs to beinverted when calculating the MMSE weighting matrix W(m).

$\begin{matrix}\begin{matrix}{{\overset{\sim}{\Lambda}(m)} = \begin{bmatrix}{\overset{\sim}{\lambda}}_{0,0} & {\overset{\sim}{\lambda}}_{0,1} & \ldots & {\overset{\sim}{\lambda}}_{0,{N_{r} - 1}} \\{\overset{\sim}{\lambda}}_{1,0} & {\overset{\sim}{\lambda}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\overset{\sim}{\lambda}}_{{N_{r} - 1},0} & \; & \; & {\overset{\sim}{\lambda}}_{{N_{r} - 1},{N_{r} - 1}}\end{bmatrix}} \\{= {\begin{bmatrix}{\hat{\lambda}}_{0,0} & {\hat{\lambda}}_{0,1} & \ldots & {\hat{\lambda}}_{0,{N_{r} - 1}} \\{\hat{\lambda}}_{1,0} & {\hat{\lambda}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\hat{\lambda}}_{{N_{r} - 1},0} & \; & \; & {\hat{\lambda}}_{{N_{r} - 1},{N_{r} - 1}}\end{bmatrix} +}} \\{\begin{bmatrix}{\hat{h}}_{0,0} & {\hat{h}}_{0,1} & \; & {\hat{h}}_{0,{K - 1}} \\{\hat{h}}_{1,0} & {\hat{h}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\hat{h}}_{{N_{r} - 1},0} & \; & \ldots & {\hat{h}}_{{N_{r} - 1},{K - 1}}\end{bmatrix}} \\{\begin{bmatrix}h_{0,0}^{*} & h_{1,0}^{*} & \ldots & h_{{N_{r} - 1},0}^{*} \\h_{0,1}^{*} & h_{1,1}^{*} & \; & \; \\\; & \; & \ddots & \; \\h_{0,{K - 1}}^{*} & \; & \; & h_{{N_{r} - 1},{K - 1}}^{*}\end{bmatrix}}\end{matrix} & (10)\end{matrix}$

where the frequency index m is omitted in the channel matrices. Afterthis MMSE antenna combining and equalization, the model of the observedsignal {tilde over (X)}(m) equals:

$\begin{matrix}{{{\hat{X}(m)} = {{{\overset{\sim}{H}(m)}{X(m)}} + {N_{\hat{X}}(m)}}}{where}} & (11) \\\begin{matrix}{{\hat{X}(m)} = \begin{bmatrix}{{\hat{x}}_{0}(m)} \\{{\hat{x}}_{1}(m)} \\\vdots \\{{\hat{x}}_{K - 1}(m)}\end{bmatrix}} \\{= \begin{bmatrix}{\hat{h}}_{0,1}^{*} & {\hat{h}}_{1,1}^{*} & \ldots & {\hat{h}}_{{N_{r} - 1},1}^{*} \\{\hat{h}}_{0,2}^{*} & {\hat{h}}_{1,2}^{*} & \; & \; \\\vdots & \; & \ddots & \; \\{\hat{h}}_{0,{K - 1}}^{*} & \; & \; & {\hat{h}}_{{N_{r} - 1},{K - 1}}^{*}\end{bmatrix}} \\{{\left( \begin{bmatrix}{\overset{\sim}{\lambda}}_{0,0} & {\overset{\sim}{\lambda}}_{0,1} & \ldots & {\overset{\sim}{\lambda}}_{0,{N_{r} - 1}} \\{\overset{\sim}{\lambda}}_{1,0} & {\overset{\sim}{\lambda}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\overset{\sim}{\lambda}}_{{N_{r} - 1},0} & \; & \; & {\overset{\sim}{\lambda}}_{{N_{r} - 1},{N_{r} - 1}}\end{bmatrix} \right)^{- 1}\begin{Bmatrix}y_{0} \\y_{1} \\\vdots \\y_{N_{r} - 1}\end{Bmatrix}}}\end{matrix} & (12) \\{and} & \; \\\begin{matrix}{{\overset{\sim}{H}(m)} = {{W^{*}(m)}{\hat{H}(m)}}} \\{= {{{\hat{H}}^{*}(m)}{{\overset{\sim}{\Lambda}}^{- 1}(m)}{\hat{H}(m)}}} \\{= \begin{bmatrix}{{\overset{\sim}{h}}_{0,0}(m)} & {{\overset{\sim}{h}}_{0,1}(m)} & \ldots & {{\overset{\sim}{h}}_{0,{K - 1}}(m)} \\{{\overset{\sim}{h}}_{1,0}(m)} & {{\overset{\sim}{h}}_{1,1}(m)} & \; & \; \\\vdots & \; & \ddots & \; \\{{\overset{\sim}{h}}_{{K - 1},0}(m)} & \; & \; & {{\overset{\sim}{h}}_{{K - 1},{K - 1}}(m)}\end{bmatrix}}\end{matrix} & (13)\end{matrix}$

Which is a channel estimate after this MMSE antenna combining andequalization. It is noted that the number of observation signals afterthe MMSE antenna combining and equalization equals the number K oftransmitters 5 ₁, . . . , 5 _(i), . . . , 5 _(K).

IDFT—Inverse Discrete Fourier Transform

Since the modulated symbols transmitted on the uplink are pre-coded by aDFT means 6, as was described with reference to FIG. 2, the symbolsafter MMSE combining and equalization must be transformed to the timedomain. Next step of the demodulator is thus the IDFT:

$\begin{matrix}{{{\overset{\sim}{s}}_{k}(n)} = {\frac{1}{\sqrt{N_{c}}}{\sum\limits_{m = 0}^{N_{c} - 1}\; {{\hat{x}(m)}^{j\frac{2\; \pi \; n\; m}{N_{c}}}}}}} & (14)\end{matrix}$

for each user, 0≦k≦K−1 and symbol 0≦n≦N_(c)−1. In a detection and softvalue calculation, which will be described next, only the channel at lagzero can be considered. This time domain channel estimate is calculatedas

$\begin{matrix}\begin{matrix}{\overset{\sim}{G} = {\frac{1}{N_{c}}{\sum\limits_{m = 0}^{N_{c} - 1}\; {\overset{\sim}{H}(m)}}}} \\{= \begin{bmatrix}{\overset{\sim}{g}}_{0,0} & {\overset{\sim}{g}}_{0,1} & \ldots & {\overset{\sim}{g}}_{0,{K - 1}} \\{\overset{\sim}{g}}_{1,0} & {\overset{\sim}{g}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\overset{\sim}{g}}_{{K - 1},0} & \; & \; & {\overset{\sim}{g}}_{{K - 1},{K - 1}}\end{bmatrix}} \\{= {\frac{1}{N_{c}}{\sum\limits_{m = 0}^{N_{c} - 1}\; \begin{bmatrix}{{\overset{\sim}{h}}_{0,0}(m)} & {{\overset{\sim}{h}}_{0,1}(m)} & \ldots & {{\overset{\sim}{h}}_{0,{K - 1}}(m)} \\{{\overset{\sim}{h}}_{1,0}(m)} & {{\overset{\sim}{h}}_{1,1}(m)} & \; & \; \\\vdots & \; & \ddots & \; \\{{\overset{\sim}{h}}_{{K - 1},0}(m)} & \; & \; & {{\overset{\sim}{h}}_{{K - 1},{K - 1}}(m)}\end{bmatrix}}}}\end{matrix} & (15)\end{matrix}$

which is a single K×K matrix. After this IDFT, a time domain model ofthe observation signal can be written as

{tilde over (S)}(n)={tilde over (G)}S(n)+N _({tilde over (S)})(n)  (16)

Scaling

Before detection and soft value calculation, which will be describedlater, a scaling of the observed signals can be done such that theresidual noise variance is unity in each of the observation signals. Bymeans of this scaling of the observed signals, divisions are avoided inthe large amount of soft value calculations.

The residual noise contains two components: additive noise N(m) filteredthrough the above-described MMSE combining weights, and inter-symbolinterference (ISI). An estimate of the filtered noise covariance matrixequals

$\begin{matrix}{\Lambda_{N} = {\sum\limits_{m = 0}^{N_{c}}\; {{W^{*}(m)}\hat{\Lambda}\; {W(m)}}}} & (17)\end{matrix}$

where W(m) are the MMSE combining matrices. The inter-symbolinterference covariance matrix equals

$\begin{matrix}{\Lambda_{ISI} = {\sum\limits_{m = 0}^{N_{c}}\; {\left( {{\overset{\sim}{H}(m)} - \overset{\sim}{G}} \right)\left( {{\overset{\sim}{H}(m)} - \overset{\sim}{G}} \right)^{*}}}} & (18)\end{matrix}$

where subtraction of G corresponds to a single tap time domain channelas calculated and shown under the previous subheading “IDFT—inversediscrete Fourier transform”.

In total, the residual noise covariance equals

$\begin{matrix}{\overset{\sim}{L} = {{\Lambda_{N} + \Lambda_{ISI}} = \begin{bmatrix}\sigma_{00}^{2} & \sigma_{01}^{2} & \ldots & \sigma_{0K}^{2} \\\sigma_{10}^{2} & \sigma_{11}^{2} & \; & \; \\\vdots & \; & \ddots & \; \\\sigma_{K0}^{2} & \; & \; & \sigma_{KK}^{2}\end{bmatrix}}} & (19)\end{matrix}$

Observation signals and channel estimates can now be scaled as

$\begin{matrix}\begin{matrix}{{\hat{S}(n)} = {\left( {{Diag}\left\{ \overset{\sim}{L} \right\}} \right)^{{- 1}/2}{\overset{\sim}{S}(n)}}} \\{= {\begin{bmatrix}{1/\sigma_{0,0}} & 0 & \ldots & 0 \\0 & {1/\sigma_{1,1}} & \; & \; \\\vdots & \; & \ddots & \; \\0 & \ldots & \; & {1/\sigma_{{K - 1},{K - 1}}}\end{bmatrix}\begin{bmatrix}{{\overset{\sim}{s}}_{0}(n)} \\{{\overset{\sim}{s}}_{1}(n)} \\\vdots \\{{\overset{\sim}{s}}_{K - 1}(n)}\end{bmatrix}}}\end{matrix} & (20) \\{and} & \; \\\begin{matrix}{\hat{G} = {\left( {{Diag}\left\{ \overset{\sim}{L} \right\}} \right)^{{- 1}/2}\overset{\sim}{G}}} \\{= \begin{bmatrix}{\hat{g}}_{0,0} & {\hat{g}}_{0,1} & \ldots & {\hat{g}}_{0,{K - 1}} \\{\hat{g}}_{1,0} & {\hat{g}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\hat{g}}_{{K - 1},0} & \; & \; & {\hat{g}}_{{K - 1},{K - 1}}\end{bmatrix}} \\{= \begin{bmatrix}{1/\sigma_{0,0}} & 0 & \ldots & 0 \\0 & {1/\sigma_{1,1}} & \; & \; \\\vdots & \; & \ddots & \; \\0 & \; & \; & {1/\sigma_{{K - 1},{K - 1}}}\end{bmatrix}} \\{\begin{bmatrix}{\overset{\sim}{g}}_{0,0} & {\overset{\sim}{g}}_{0,1} & \ldots & {\overset{\sim}{g}}_{0,{K - 1}} \\{\overset{\sim}{g}}_{1,0} & {\overset{\sim}{g}}_{1,1} & \; & \; \\\vdots & \; & \ddots & \; \\{\overset{\sim}{g}}_{{K - 1},0} & \; & \; & {\overset{\sim}{g}}_{{K - 1},{K - 1}}\end{bmatrix}}\end{matrix} & (21)\end{matrix}$

respectively, such that the resulting time domain model of the signalequals

Ŝ(n)=ĜS(n)+N _(Ŝ)(n)  (22)

where N_(Ŝ)(n) is a spatially uncorrelated and white noise, withcovariance matrix equal to identity matrix.

QR Factorization

In the Maximum Likelihood Detector (MLD) to be described under the nextsubheading, the computational complexity will be shown to increaseexponentially with both the number of bits per symbol and the number ofusers. In order to reduce this computational complexity, a QRfactorization of the time domain channel may be calculated such that theM-algorithm as described later on (under the subheading “M-algorithm”)can be used. This QR factorization is calculated from the time domainchannel estimate Ĝ as

Ĝ=Q·R  (23)

such that Q is unitary matrix, i.e. QQ*=Q*Q=I, and R is uppertriangular. By multiplying the observed signal Ŝ(n) with Q*, the channelis transformed to be upper triangular,

Ŝ _(QR)(n)=Q*Ŝ(n)=Q*ĜS(n)+Q*N _({tilde over (S)}) =Ĝ _(QR) S(n)+N_(QR)(n)  (24)

where Ĝ_(QR)=R is introduced. This transformation does not change thenegative Log Likelihood

∥Ŝ(n)−ĜS(n)∥²=(Ŝ(n)−ĜS(n))*QQ*(Ŝ(n)−ĜS(n))=∥Ŝ _(QR)(n)−Ĝ _(QR)S(n)∥²  (25)

as is used in the joint detection and soft value calculations to bedescribed next.

Joint Detection and Soft Value Calculation

Soft value calculations, i.e. some probability calculations regardingthe probability that the observed bit is actually equal to thetransmitted bit now have to be performed. The algorithms for calculatingthe soft values to be used in the decoder will be described in thefollowing.

First, a Maximum Likelihood Detector (MLD) is described for which in ajoint detection context, a criterion is evaluated with hypotheses testcandidates of all possible transmitted symbols for all users.Thereafter, an M-algorithm is described, for which a selection is doneof which transmitted symbols to evaluate.

Maximum Likelihood Detector

The M-algorithm requires the channel matrix to be upper triangular,which is the result from the QR factorization described above.

However, it is noted that the MLD to be described could be used withoutthe QR algorithms in which case Ĝ_(QR) can be replaced by Ĝ andŜ_(QR)(n) with Ŝ(n). All symbols of all users then have to be evaluatedfor all combinations. It is further noted that if no QR factorization isperformed then the M-algorithm cannot be used.

For the maximum likelihood detector to be described below, and in thecontext of joint detection, a criterion is evaluated with hypothesistest candidates of all possible transmitted symbols for all users.

The soft value, for bit number i and user k is calculated, for example,as the Log Likelihood Ratio (LLR) with squared Euclidian distances

$\begin{matrix}{{L\left( {b_{k}(i)} \middle| {\hat{S}}_{QR} \right)} = {{\underset{S \in S_{0,k,i}}{\min\limits_{}}\left\{ {{{\hat{S}}_{QR} - {{\hat{G}}_{QR}S}}}^{2} \right\}} - {\underset{S \in S_{1,k,i}}{\min\limits_{}}\left\{ {{{\hat{S}}_{QR} - {{\hat{G}}_{QR}S}}}^{2} \right\}}}} & (26)\end{matrix}$

where b_(k)(i) is bit number I for user number k, and S_(0,i,k) is theset of all possible transmitted symbols for which bit number i is “0”for user k. Correspondingly, S_(1,i,k) is the set of all possibletransmitted symbols for which bit number i is “1” for user k. Thisnegative log likelihood ∥Ŝ_(QR)−Ĝ_(QR)S∥² is often referred to as theMLD metric and Ŝ_(QR)−Ĝ_(QR)S as MLD residuals.

As another example, LLR with Euclidian distances could be used forcalculating the soft value

$\begin{matrix}{{L\left( {b_{k}(i)} \middle| {\hat{S}}_{QR} \right)} = {{\underset{S \in S_{0,k,i}}{\min\limits_{}}\left\{ {{{\hat{S}}_{QR} - {{\hat{G}}_{QR}S}}} \right\}} - {\underset{S \in S_{1,k,i}}{\min\limits_{}}\left\{ {{{\hat{S}}_{QR} - {{\hat{G}}_{QR}S}}} \right\}}}} & (27)\end{matrix}$

In a system with K users and P bits per symbol, and for differentmodulation algorithms (illustrated in FIGS. 5 a-5 c)

BPSK (binary phase shift keying): P=1QPSK (quadrature phase shift keying, FIG. 5 a): P=216-QAM (16-quadrature amplitude modulation, FIG. 5 b): P=464-QAM (FIG. 5 c): P=6the number of candidates, in the LLR is

N _(states)=(2^(P))^(K)  (28)

For example, with two user equipments, i.e. K=2, and QPSK, the number ofcandidates is 16 and the total set of all possible transmitted symbolsis

$\begin{matrix}{S_{total} = {\frac{1}{\sqrt{2}}\left\{ {{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{1 + j} \\{1 + j}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{1 + j} \\{1 - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 + j} \\{{- 1} + j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 + j} \\{{- 1} - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 - j} \\{1 + j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 - j} \\{1 - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 - j} \\{{- 1} + j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1 - j} \\{{- 1} - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{{- 1} + j} \\{1 + j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{{- 1} + j} \\{1 - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{{- 1} + j} \\{{- 1} + j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{{- 1} + j} \\{{- 1} - j}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{{- 1} - j} \\{1 + j}\end{matrix} \right\rbrack}\begin{bmatrix}{{- 1} - j} \\{1 - j}\end{bmatrix}}\begin{bmatrix}{{- 1} - j} \\{{- 1} + j}\end{bmatrix}}\begin{bmatrix}{{- 1} - j} \\{{- 1} - j}\end{bmatrix}} \right\}}} & (29)\end{matrix}$

with corresponding bits

$\begin{matrix}{B_{total} = {\frac{1}{\sqrt{2}}\left\{ {{{{{{{{{{{{{{{\left\lbrack \begin{matrix}{0,0} \\{0,0}\end{matrix} \right\rbrack\left\lbrack \begin{matrix}{0,0} \\{0,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,0} \\{1,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,0} \\{1,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,1} \\{0,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,1} \\{0,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,1} \\{1,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{0,1} \\{1,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,0} \\{0,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,0} \\{0,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,0} \\{1,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,0} \\{1,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,1} \\{0,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,1} \\{0,1}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,1} \\{1,0}\end{matrix} \right\rbrack}\left\lbrack \begin{matrix}{1,1} \\{1,1}\end{matrix} \right\rbrack} \right\}}} & (30)\end{matrix}$

As an example, the set S_(1,0,0) (for which the bit is equal to “1”, foruser zero and bit number zero) is the set containing element number 8,9, 10, 11, 12, 13, 14 and 15 in S_(total). FIGS. 5 a-5 c thusillustrates the mapping between symbols and bits, for QPSK, 16 QAM and64 QAM symbol constellations, respectively.

M-Algorithm

If the QR-algorithm as described earlier is used, the channel matrixĜ_(QR) is upper triangular, as mentioned earlier. Then the MLD residualsused in the Log Likelihood Ratio (LLR) metrics equals

$\begin{matrix}\begin{matrix}{{E(n)} = {{{{\hat{S}}_{QR}(n)} - {{\hat{G}}_{QR}{S( n)}}} =}} \\{= {\left\lbrack \begin{matrix}{{\hat{s}}_{{QR},0}(n)} \\{{\hat{s}}_{{QR},1}(n)} \\\vdots \\{{\hat{s}}_{{QR},{K - 2}}(n)} \\{{\hat{s}}_{{QR},{K - 1}}(n)}\end{matrix} \right\rbrack -}} \\{{\left\lbrack \begin{matrix}{\hat{g}}_{{QR},0,0} & {\hat{g}}_{{QR},0,1} & \ldots & \; & {\hat{g}}_{{QR},0,{K - 1}} \\0 & {\hat{g}}_{{QR},1,1} & \; & \; & \vdots \\\vdots & \; & \ddots & {\hat{g}}_{{QR},{K - 2},{K - 2}} & {\hat{g}}_{{QR},{K - 2},{K - 1}} \\0 & 0 & \ldots & 0 & {\hat{g}}_{{QR},{K - 1},{K - 1}}\end{matrix} \right\rbrack \begin{bmatrix}{s_{0}(n)} \\{s_{1}(n)} \\\; \\{s_{K - 2}(n)} \\{s_{K - 1}(n)}\end{bmatrix}}}\end{matrix} & (31)\end{matrix}$

such that the observation ŝ_(QR,K−1)(n) depends only on s_(K−1)(n). In afirst step of an M-algorithm, metric values equal to the absolute squareof the MLD residual are calculated for the last row only. Here, metricvalues are calculated for all possible candidates of s_(K−1)(n). This isillustrated in FIG. 6, in step 1. Further, the M candidates ofs_(K−1)(n) are determined which yields the lowest metric. These symbolsare defined as surviving candidates. In the next step, step 2, oneadditional value of the observation signal ŝ_(QR,K−2)(n) is used and theresiduals are calculated for all possible transmitted candidates ofs_(K−2)(n) but only with the M surviving candidates from the previousstep. This procedure is then repeated, step 3, until all observationsignals are included, where only M symbols as surviving candidates aftereach step. FIG. 6 thus illustrates an example of the QRM-MLD algorithmfor M=2, QPSK (P=2) and three users (K=3).

The above-described steps provide a filtered signal from the receivedcommunication signal. This filtered signal is input to the final step ofthe demodulator 17, comprising demodulation means for demodulating ordecoding the filtered signal in order to recover the transmitted databits.

When LLR soft values are calculated, it is likely that no survivingcandidate exists for some bit values. In the example illustrated in FIG.6, bit number one equal to “1” for user K−1, has no surviving candidatein the final third step. Different possible algorithms for calculatingsoft values in this case can be used. For example, these missing metricvalues could be replaced by a large constant, which indicates that thisbit is unlikely to have been transmitted. Alternatively, the LLR forbits, which are missing in the final step, is replaced by the metricdifference from the latest previous step in which MLD metric valuesexist. In the example illustrated in FIG. 6, metric values for bitnumber one equal to “1” for user K−1 is only calculated in the firststep. The LLR is in this case calculated by only considering theobservation s_(K−1)(n). Yet further algorithms for calculating softvalues for bits lacking surviving candidates are conceivable.

Simulation Results

Simulations have been performed on the performance of uplink LTE, interms of BLER (block error rate), using the MMSE equalizer as describedabove.

When comparing single detection and joint detection, the simulationresults showed that with a single user equipment, there was nosignificant difference. The results further indicated that theperformance increased for joint detection compared to single detectionas the number of concurrent user equipments increases.

Simulations have also been done for LLR soft value calculations based onboth Euclidian and squared Euclidian distances, using varying number ofsurvivor candidates M. The results indicate no difference between thetwo LLR variants for MLD and QRM with M=16. When the number of survivorcandidates is decreased to M=8, then the QRM performance degradecompared to MLD. In this case the Euclidian distance in the LLR showedbetter performance compared to squared Euclidian distance.

The present invention can be generalized, which will be described in thefollowing. The above embodiment of the present invention can beconsidered a special case of the generalized idea of the invention, andmore particularly, the scaling step can be replaced with a whiteningstep. This is realized by noticing that scaling is a special case ofwhitening, wherein only the elements of the main diagonal from awhitening matrix are used.

Thus, while the scaling described above uses only the diagonal elementsof the whitening matrix, this embodiment comprises the use of the entirewhitening matrix.

In short, the invention when generalized provides a reduced-complexityML detection for SC-FDMA systems, the detection comprising the steps ofequalization, whitening filtering and ML detection. In accordance withthe invention, the output of the equalization step is divided intoseveral smaller parts, each of which is taken as the input to the MLdetection step. Stated differently, ML detection is performed not overthe entire SC-FDMA symbol, but only over a part of the SC-FDMA symbol.Recall that a SC-FDMA symbol comprises multiple layers in the spacedomain and multiple time instants in the time domain. Therefore, avariety of ways of defining the input to ML detection (at the output ofthe equalization step) is made possible.

In the following, each layer at a time instant (at the output of theequalization step) is represented by each element of a vector symbol. Asthe simplest example, all (or some) of the layers at a time instant canbe taken as the input to ML detection. In other words, the ML detectionis carried out over each vector symbol (or some elements of a vectorsymbol) from the equalization (ML detection in space domain).

In addition all (or some) of the time instants within a SC-FDMA symbolat a layer can be taken as the input to ML detection and, in this case,the elements at the same location of all (or some) vector symbols arejointly detected (ML detection in time domain).

It is noted that the ML detection may be performed in a hybrid fashion,e.g. in both space and time domains. For example, the ML detection canbe applied to the first two layers at two consecutive time instants andthe second two layers at the same instants separately. Since thenoise-plus-interference at the input of the ML detection is generallycorrelated, the whitening step should be placed in between the step ofequalization and the step of ML detection. The whitening step (whiteningfilter) plays the role of de-correlating the noise-plus-interference andthe coefficient is determined by the definition of the input to the MLdetection.

In the following, MIMO SC-FDMA is assumed. As mentioned above, variousways of defining the input of the ML detection are possible, but in thefollowing focus is concentrated on the case where all the layers, ormore accurately, all the corresponding modulation symbols, at a timeinstant at the output of the equalization (represented by a vectorsymbol) are taken as the input to the step of ML detection. It is notedthat most of the following description is applicable to any otherdefinitions of the input to the step of ML detection. For example, thedescription is applicable to the case where all (or some) of themodulation symbols at a layer are taken as the input to the step of MLdetection.

Assume that there are N_(t) transmit antennas and N_(r) receiveantennas, and that each SC-FDMA symbol comprises R layers and Ksubcarriers. Further, assume that the step of equalization compriseslinear equalization (LE). The output of the LE corresponding to aSC-FDMA symbol is expressed as

$\begin{matrix}{{{\overset{\sim}{s} = {\left( {F_{K}^{*} \otimes I_{R}} \right)\left( {{E^{*}R_{w}^{- 1}E} + {\frac{1}{\alpha \; K}I_{RK}}} \right)^{- 1}E^{*}R_{w}^{- 1}{E\left( {F_{K} \otimes I_{R}} \right)}}}\quad}{s++}\frac{1}{\sqrt{\alpha \; K}}\left( {F_{K}^{*} \otimes I_{R}} \right)\left( {{E^{*}R_{w}^{- 1}E} + {\frac{1}{\sqrt{\alpha \; K}}I_{RK}}} \right)^{- 1}E^{*}R_{w}^{- 1}w} & (32)\end{matrix}$

whereF_(K) is an K×K matrix representing the normalized DFT, and F*_(K) isthe conjugate transpose thereof,E is an N_(r)K×RK matrix representing the equivalent channel (includingthe precoder) and E* is the conjugate transpose thereof,s is an RK×1 vector representing the transmitted symbols where s=(s₀^(T) . . . s_(K−1) ^(T))^(T) and s_(k) is an R×1 column vector,w is an N_(r)K×1 vector representing the noise symbols,R_(w)=E{ww*} is an N_(r)K×N_(r)K matrix representing the noisecovariance and

denotes the Kronecker product.

It is noted that F_(K)

I_(R), F*_(K)

I_(R) and

$\left( {{E^{*}R_{w}^{- 1}E} + {\frac{1}{\alpha \; K}I_{RK}}} \right)^{- 1}E^{*}R_{w}^{- 1}$

in equation (B) represent per-layer DFT, per layer IDFT andper-subcarrier LE (MMSE) within a SC-FDMA symbol, respectively. It isfurther noted that the transmit power is normalized through α, which isdefined as

$\begin{matrix}{\alpha = {\frac{N}{K}\frac{E_{s}}{N_{t}}}} & (33)\end{matrix}$

whereN is the total number of subcarriersE_(s) is the received energy per subcarrier

The noise is assumed to be spatially correlated between the antennabranches, but temporally uncorrelated, and the correlation istime-invariant. Therefore, letting w_(k) denote the R×1 vector symbolrepresenting the noise symbols for the k-th subcarrier, the covariancematrix R_(w) _(K) =E{w_(k)w*_(k)} is related to R_(w) as

R _(w)=diag(R _(w) ₀ , R _(w) ₁ , . . . , R _(w) _(K−1) )  (34)

It is noted that since each subcarrier experiences frequency-flat fadingdue to the orthogonality, the equivalent channel matrix E is ablock-diagonal matrix expressed as

E=diag(E ₀ , E ₁ , . . . , E _(K−1))  (35)

where an N_(r)×R matrix E_(k) represents the equivalent channel(including the precoder) at the k-th subcarrier. Using the followingdefinitions

$\begin{matrix}{P = {{\left( {{E^{*}R_{w}^{- 1}E} + {\frac{1}{\alpha \; K}I_{RK}}} \right)^{- 1}E^{*}R_{w}^{- 1}E} = {{diag}\left( {P_{0},P_{1},\ldots \mspace{14mu},\mspace{14mu} P_{K - 1}} \right)}}} & (36) \\{Q = {{\left( {{E^{*}R_{w}^{- 1}E} + {\frac{1}{\alpha \; K}I_{RK}}} \right)^{- 1}E^{*}R_{w}^{- 1}E} = {{diag}\left( {Q_{0},Q_{1},\ldots \mspace{14mu},\mspace{14mu} Q_{K - 1}} \right)}}} & (37)\end{matrix}$

the k-th vector symbol at the output of the linear equalization step maybe expressed as

$\begin{matrix}{{\overset{\sim}{s}}_{k} = {{\left( {\frac{1}{K}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}}} \right)s_{k}} + \eta_{k}}} & (38)\end{matrix}$

where the covariance of noise-plus-interference R_(η) _(k)=E{η_(k)η*_(k)} is given by

$\begin{matrix}{R_{\eta_{k}} = {{\frac{1}{\alpha \; K^{2}}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; \left( {{\alpha \; {KP}_{k^{\prime}}P_{k^{\prime}}^{*}} + {Q_{k^{\prime}}R_{w_{k^{\prime}}}Q_{k^{\prime}}^{*}}} \right)}} - {\frac{1}{K^{2}}\left( {\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}} \right)\left( {\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}} \right)^{*}}}} & (39)\end{matrix}$

In the output from the linear equalization step, the gain of the desiredsignal is denoted by

$\begin{matrix}{G = {\frac{1}{K}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}}}} & (40)\end{matrix}$

which is the resulting channel after linear equalization. This is asingle tap channel model, i.e. instead of having an impulse response inthe time domain, only the impulse response for time lag zero is used.

If R_(η) _(k) is expressed as (e.g. using Cholesky decomposition)

R_(η) _(k) ⁻¹=LL*  (41)

then the coefficients of the whitening filter are given by L*, and theoutput of the whitening filter, i.e. the input to the ML detection step,can be expressed as

$\begin{matrix}{x_{k} = {{L^{*}{\overset{\sim}{s}}_{k}} = {{{L^{*}\left( {\frac{1}{K}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}}} \right)}s_{k}} + {L^{*}\eta_{k}}}}} & (42)\end{matrix}$

It is noted that the resulting noise-plus-interference e_(k)=L*_(η) _(k)is completely whitened, since

R _(e) _(k) =E{e _(k) e* _(k) }=L*E{η _(k)η*_(k) }L=L*R _(η) _(k) L=I_(R)  (43)

The complexity can be further reduced by approximating the whiteningfilter by a diagonal matrix whose diagonal entries are taken from thoseof L*, which would result in the scaling-case described initially.

It is noted that the ML detection takes

$L^{*}\left( {\frac{1}{K}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}}} \right)$

as its channel matrix. For example, QRM-MLD (described earlier for thescaling case) starts with the QR decomposition given by

$\begin{matrix}{{L^{*}\left( {\frac{1}{K}{\sum\limits_{k^{\prime} = 0}^{K - 1}\; P_{k^{\prime}}}} \right)} = {QR}} & (44)\end{matrix}$

where Q is a unitary matrix (i.e. Q*Q=QQ*=I=“identity matrix”) and R isupper triangular. This decomposition is calculated such that the channelL*G after linear equalization and whitening can be written as a productof Q and R. In a QRM-MLD approach, a signal is multiplied with Q*, suchthat the resulting channel equals R. In the present invention, theoutput of the linear equalization and the whitening filter x_(k) ismultiplied with Q*, such that the gain of the desired signal now equalsR.

As mentioned earlier, ML detection over the entire SC-FDMA symbol alwaysminimizes the error probability. The method in accordance with theinvention thus shows some performance loss as the ML detection takesonly a part of the output of the LE step as the input. However, giventhis limitation of parts given to the detection, the method inaccordance with the invention provides the minimum error probability,since it whitens the noise-plus-interference at the input of MLdetection. Subsequently, according to the ML detection rule under theassumption of additive Gaussian noise, minimizes the absolute squarevalue of the residual, i.e. difference, between received signal andhypothesis testing of all possible transmitted symbols. It is noted thatby means of the whitening step, i.e. by passing through the whiteningfilter, it is possible to directly apply the conventional ML detectionthat assumes uncoloured (white) noise-plus-interference at the input.

As described above, the invention utilizes a conventional linearequalization to decompose the modulation symbols within a SC-FDMA symboland performs ML detection over a part of the modulation symbols, insteadof performing ML detection over the entire SC-FDMA symbol. The whiteningfiltering between the linear equalization and the ML detection plays arole of removing the correlation of noise-plus-interference signalinduced by the equalization.

Briefly comparing the first embodiment of the invention and thegeneralized concept, the equation (19) corresponds to equation (39), andequation (20) corresponds to equation (42). The results from theseequations are then used in a corresponding manner, i.e. the signal andthe channel are both multiplied with the result (Diag{{tilde over(L)}})^(−1/2) and L*, respectively.

The invention thus provides a reduced-complexity ML detection forSC-FDMA: equalization is followed by ML detection. The equalizationcould for example be linear equalization (LE) or decision feedbackequalization (DFE), but other equalization methods are also conceivable.The output of the equalization step corresponding to a SC-FDMA symbol isdivided into several parts, each of which is taken as the input of theML detection. For example, in the case of MIMO (multiple input, multipleoutput) SC-FDMA, ML detection can be applied to either all (or some) ofthe layers at a time instant or all (or some) of the time instants at alayer. In order to whiten the correlated noise-plus-interference at theinput of the ML detection step, a whitening filter is inserted betweenthe steps of equalization and ML detection. The filter coefficients canbe calculated based on the channel coefficients (including precoder, ifany) and noise covariance. The Cholesky decomposition can be utilized tocalculate the coefficients. The invention theoretically minimizes theerror probability when the output of equalization is partiallyavailable.

With reference to FIG. 7, showing a flow chart over steps in a method 30in accordance with the invention, the above-described steps performed inthe decoder can be summarized as follows:

The communication signals are modulated, pre-coded by a discrete Fouriertransform and transmitted by means of single-carrier frequency divisionmultiple access scheme (SC-FDMA).

The method 30 comprises a first step 31 of performing an antennacombining and equalization on a signal Y(m) observed at the receiverbased on a weighting matrix W(m). Thereby a model of observed signal{circumflex over (X)}(m) and a frequency domain channel estimate {tildeover (H)}(m) are provided. The method 30 comprises a second step 32 ofperforming inverse discrete Fourier transform on the model of observedsignal {circumflex over (X)}(m), thereby providing a time domain model{tilde over (S)}(n) of the observed signal {circumflex over (X)}(m), andperforming an inverse discrete Fourier transform of the frequency domainchannel estimate {tilde over (H)}(m), thereby providing a time domainchannel estimate {tilde over (G)}(p) with length P wherein p=0, 1, . . ., P−1. The method 20 comprises the third step 33 of whitening filteringthe time domain model {tilde over (S)}(n) of the observed signal{circumflex over (X)}(m), thereby providing a whitened time domain modelŜ(n) of the time domain model {tilde over (S)}(n) and a whitened timedomain channel estimate Ĝ(p) for p=0, 1, . . . , P−1. The method 30comprises a fourth step 34 of jointly detecting the received at leasttwo communication signals by performing soft value calculations based onmaximum likelihood detection of the whitened time domain model Ŝ(n),using the whitened time domain channel estimate Ĝ(p) for p=0, 1, . . . ,P−1, whereby the received communication signals are decoded.

In accordance with an embodiment of the invention, the step of whitening33 is performed before the step of joint detection.

In accordance with another embodiment of the invention, the step ofjointly detecting 34 comprises a single tap channel model, P=1. Theinventive method is thus applicable to both single-tap channel models aswell as multi-tap channel models.

In accordance with yet another embodiment of the invention, the method30 comprises, prior to the step of jointly detecting 33, a step (notillustrated in FIG. 7) of performing QR factorization of the time domainchannel matrix estimate Ĝ, providing a QR factorized signal modelŜ_(QR)(n) and a time domain channel matrix estimate after QRfactorization Ĝ_(QR). The step of jointly detecting then comprisesdetecting the QR factorized signal model Ŝ_(QR)(n) by: calculating softvalues for bit number i and user k providing two sets of all possibletransmitted symbols S_(1,k,i), S_(0,k,i), for which transmitted bit is“1” and “0”, respectively; selecting which of the two sets of allpossible transmitted symbols S_(1,k,i), S_(0,k,i) to evaluate; andevaluating the selected possible transmitted symbols. By performing aQR-factorization, the amount of calculations is reduced even further,since the channel matrix Ĝ_(QR) is upper triangular. Thereby the use ofM-algorithm is enabled.

In accordance with still another embodiment of the invention, using theM-algorithm, the step of evaluating comprises the steps of: definingmaximum likelihood detection residuals as E(n)=Ŝ_(QR)(n)−Ĝ_(QR)S(n),where E(n)=[e₀(n) . . . e_(K−2)(n) e_(K−1)(n)]^(T),Ŝ_(QR)(n)=[ŝ_(QR,0)(n) . . . ŝ_(QR,K−1) ŝ_(QR,K−1)(n)]^(T) andS(n)=[s₀(n) . . . s_(K−2)(n) s_(K−1)(n)]^(T), whereby the residuale_(K−1)(n) only depends on observation symbol ŝ_(QR,K−1)(n) and symbolhypothesis s_(K−1)(n),

-   -   (i) calculating, for the last row of the definition, metric        values equal to the absolute square of maximum likelihood        detection residuals for all possible candidates of s_(K−1)(n),    -   (ii) determining M candidates of s_(K−1)(n), providing M        surviving candidates,    -   (iii) repeating steps (i) and (ii) for one additional value of        the observation signal ŝ_(QR,K−2)(n),    -   (iv) calculating, for the M surviving candidates, all possible        transmitted candidates of s_(K−2)(n), and    -   (v) repeating steps (iii) and (iv) for all observation signals.        The use of the M-algorithm greatly reduces the amount of        calculations required for determining, with high probability        which codeword that was most likely to have been sent. The        number of iterations can be held to a minimum.

In accordance with yet another embodiment of the invention, the step ofjointly detecting 34 comprises soft value calculations performed bymeans of Log Likelihood Ratio with squared Euclidian distances or LogLikelihood Ratio based on Euclidian distances.

In accordance with yet another embodiment of the invention, the step ofwhitening filtering 33 comprises: estimating a residualnoise-plus-interference covariance matrix R_(η) _(k) ; performingCholesky decomposition of the residual noise-plus-interferencecovariance matrix R_(η) _(k) =LL* thereby providing an lower triangularmatrix L; whitening the signal time domain model {tilde over (S)}(n) bymultiplying the signal time domain model {tilde over (S)}(n) with L*,thereby providing a whitened time domain model Ŝ(n); and whitening thetime domain channel matrix estimate {tilde over (G)} by multiplying thetime domain channel estimate {tilde over (G)} with L*, thereby providinga whitened time domain channel estimate Ĝ.

In accordance with still another embodiment of the invention, the stepof whitening 33 comprises scaling the received signal. This embodimentreduces the number of calculations required even further, but at theexpense of loosing some performance in terms of accuracy.

In accordance with yet another embodiment of the invention, the step ofscaling (special case of step 33) comprises estimating a residual noisecovariance matrix {tilde over (L)} by a sum of Λ_(N) and Λ_(ISI),wherein Λ_(N) is the noise covariance matrix of the white noise matrixN_(Ŝ)(n) and Λ_(ISI) is inter-symbol interference covariance matrix, andscaling the signal time domain model {tilde over (S)}(n) by multiplyingthe signal time domain model {tilde over (S)}(n) with (Diag{{tilde over(L)}})^(−1/2), providing a scaled time domain model Ŝ(n), and scalingthe time domain channel matrix estimate {tilde over (G)} by multiplyingthe time domain channel estimate {tilde over (G)} with (Diag{{tilde over(L)}})^(−1/2), providing a scaled time domain channel estimate Ĝ.

The antenna combining may be performed by a linear minimum mean squareerror, and/or the weighting matrix W(m) may be chosen so as to minimizea mean square error.

An important aspect of embodiments of the invention is the location ofthe function blocks. By separating the whitening function block from thejoint detection function block, a reduction in computational efforts isenabled. It is to be noted that the whitening can be performed prior toor after the QR decomposition and prior to or after the IDFT.

It is further noted that the above-described transmitter and receiverfunctions can be implemented in hardware, software or some combinationthereof, e.g. implemented by Application Specific Integrated Circuits(ASICs) or by a computer program comprising stored program instructionsto be executed for example by a microprocessor or a digital signalprocessor.

FIG. 8 illustrates a wireless radio communication system 40 comprising abase station 41 and user equipment 42, wherein the present invention maybe applied. The base station 41 comprises a receiver 43 for use in thewireless communication system 30 for communication of signals. Thereceiver 43 in turn comprises means 44 for performing the method 20described. In particular, the means 44 are intended to comprise all thenecessary means described above, i.e. boxes 12-24.

The means 34 may for example comprise Application Specific IntegratedCircuits (ASICs) or a computer program comprising stored programinstructions to be executed by a microprocessor or a digital signalprocessor.

In summary, the invention enables a reduced complexity ML detection forSC-FDMA. Firstly, the invention theoretically minimizes the errorprobability, when the output of equalization is partially available,i.e. it is divided into several smaller parts and each part is taken asthe input of the detector. Secondly, since ML detection is applied to apart of a SC-FDMA symbol, instead of the entire SC-FDMA symbol, it ispossible to significantly reduce the resulting computational complexity,depending on the definition of the input of ML detection. For example,if ML detection is carried out for each vector symbol from the linearequalization step, the number of hypotheses amounts to 16 (4²), assumingthe transmission of 2 layers modulated by QPSK. In addition, thewhitening step leads to additional computational complexity, as comparedto OFDM, but it amounts to only a small faction of the total complexity.Furthermore, thanks to the single-carrier property of SC-FDMA, thecalculation should be done only once per SC-FDMA symbol. Thirdly, sincethe whitening filtering removes the correlation ofnoise-plus-interference, most of the state-of-the-art ML detectionschemes are applicable. Fourthly, the invention provides flexibilityregarding performance versus complexity trade-offs in accordance withthe definition of the input to the ML detection. For example, if MLdetection is performed jointly for two consecutive vector symbols, thenumber of hypotheses increases to 256 (=4⁴) in the above example. SinceML detection is applied to two consecutive symbols instead of one symbolfrom the output of the linear equalization, in this example, theresulting performance is expected to improve, compared toper-vector-symbol ML detection. By including more and more consecutivesymbols, the performance is expected to continue to improve, but at anincreasing computational cost. It is noted that, as mentioned earlier,the present invention is quite generally applicable to any part of theoutput of the linear equalization. For example, the first and secondelements of two consecutive vector symbols, i.e. the two first layers oftwo consecutive samples, can be taken as the input to the ML detection,where the number of hypotheses amount to 256 (=4⁴).

Finally, some advantages of the invention are summarized in thefollowing:

-   -   The error probability is optimized, when the output of        equalization is partially available,    -   The computational complexity is reasonable,    -   Thanks to whitening filtering, most of the state-of-the-art ML        detection schemes are applicable,    -   A flexible trade-off between error performance and computational        complexity is rendered possible.

1. A method in a receiver for decoding at least two receivedcommunication signals, said communication signals being modulated,pre-coded by a discrete Fourier transform and transmitted by means ofsingle-carrier frequency division multiple access scheme (SC-FDMA), saidmethod comprising the steps of: performing an antenna combining andequalization on a signal Y(m) observed at said receiver based on aweighting matrix W(m), providing a model of observed signal {circumflexover (X)}(m) and a frequency domain channel estimate {tilde over(H)}(m), performing inverse discrete Fourier transform on said model ofobserved signal {circumflex over (X)}(m), providing a time domain model{tilde over (S)}(n) of said observed signal {circumflex over (X)}(m),and an inverse discrete Fourier transform of said frequency domainchannel estimate {tilde over (H)}(m) providing a time domain channelestimate {tilde over (G)}(p) with length P wherein p=0, 1, . . . , P−1,whitening said time domain model {tilde over (S)}(n) of said observedsignal {circumflex over (X)}(m), providing a whitened time domain modelŜ(n) of said time domain model {tilde over (S)}(n) and a whitened timedomain channel estimate Ĝ(p) for p=0, 1, . . . , P−1, and jointlydetecting said received at least two communication signals by performingsoft value calculations based on maximum likelihood detection of saidwhitened time domain model Ŝ(n) using said whitened time domain channelestimate Ĝ(p) for p=0, 1, . . . , P−1, whereby said at least tworeceived communication signals are decoded.
 2. The method as claimed inclaim 1, wherein said step of whitening is performed prior to said stepof jointly detecting.
 3. The method as claimed in claim 1, wherein saidstep of whitening is performed prior to said step of performing inversediscrete Fourier transform.
 4. The method as claimed in claim 1, whereinsaid step of jointly detecting comprises a single tap channel model,P=1.
 5. The method as claimed in claim 1, comprising, prior to said stepof jointly detecting, a step of performing QR factorization of said timedomain channel matrix estimate Ĝ, providing a QR factorized signal modelŜ_(QR)(n) and a time domain channel matrix estimate after QRfactorization Ĝ_(QR), and wherein said step of jointly detectingcomprises detecting said QR factorized signal model Ŝ_(QR)(n) by:calculating soft values for bit number i and user k providing two setsof all possible transmitted symbols S_(1,k,i), S_(0,k,i), for whichtransmitted bit is “1” and “0”, respectively, selecting which of saidsets of all possible transmitted symbols S_(1,k,i), S_(0,k,t) toevaluate, and evaluating said selected possible transmitted symbols. 6.The method as claimed in claim 5, wherein said step of evaluatingcomprises the steps of: defining maximum likelihood detection residualsas E(n)=Ŝ_(QR)(n)−Ĝ_(QR)S(n), where E(n)=[e₀(n) . . . e_(K−2)(n)e_(K−1)(n)]^(T), Ŝ_(QR)(n)=[ŝ_(QR,0)(n) . . . ŝ_(QR,K−2)ŝ_(QR,K−1)(n)]^(T) and S(n)=[s₀(n) . . . s_(K−2)(n) s_(K−1)(n)]^(T),whereby the residual e_(K−1)(n) only depends on observation symbolŝ_(QR,K−1)(n) and symbol hypothesis s_(K−1)(n), (i) calculating, for thelast row of said definition, metric values equal to the absolute squareof maximum likelihood detection residuals for all possible candidates ofs_(K−1)(n), (ii) determining M candidates of s_(K−1)(n), providing Msurviving candidates, (iii) repeating steps (i) and (ii) for oneadditional value of said observation signal ŝ_(QR,K−2)(n), (iv)calculating, for said M surviving candidates, all possible transmittedcandidates of s_(K−2)(n), and (v) repeating steps (iii) and (iv) for allobservation signals.
 7. The method as claimed in claim 1, wherein saidstep of jointly detecting comprises soft value calculations performed bymeans of Log Likelihood Ratio with squared Euclidian distances or LogLikelihood Ratio based on Euclidian distances.
 8. The method as claimedin claim 1, wherein said step of whitening comprises: estimating aresidual noise-plus-interference covariance matrix R_(η) _(k) ,performing Cholesky decomposition of said residualnoise-plus-interference covariance matrix R_(η) _(k) =LL*, providing alower triangular matrix L whitening said signal time domain model {tildeover (S)}(n) by multiplying said signal time domain model {tilde over(S)}(n) with L*, providing a whitened time domain model Ŝ(n), andwhitening said time domain channel matrix estimate {tilde over (G)} bymultiplying said time domain channel estimate {tilde over (G)} with L*,providing a whitened time domain channel estimate Ĝ.
 9. The method asclaimed in claim 1, wherein said step of whitening comprises scalingsaid received signal with (Diag{R_(η) _(k) })^(−1/2).
 10. The method asclaimed in claim 9, wherein said step of scaling comprises: estimating aresidual noise covariance matrix {tilde over (L)}by a sum of Λ_(N) andΛ_(ISI), wherein Λ_(N) is the noise covariance matrix of said whitenoise matrix N_(Ŝ)(n) and Λ_(ISI) is inter-symbol interferencecovariance matrix, and scaling said signal time domain model {tilde over(S)}(n) by multiplying said signal time domain model {tilde over (S)}(n)with (Diag {{tilde over (L)}})^(−1/2), providing a scaled time domainmodel Ŝ(n), and scaling said time domain channel matrix estimate {tildeover (G)} by multiplying said time domain channel estimate {tilde over(G)}with (Diag {{tilde over (L)}})^(−1/2), providing a scaled timedomain channel estimate Ĝ.
 11. The method as claimed in claim 1, whereinsaid weighting matrix W(m) is chosen so as to minimize a mean squareerror.
 12. A receiver for use in a radio communication system forcommunication of signals, comprising means for performing a methodcomprising: performing an antenna combining and equalization on a signalY(m) observed at said receiver based on a weighting matrix W(m),providing a model of observed signal {circumflex over (X)}(m) and afrequency domain channel estimate {tilde over (H)}(m), performinginverse discrete Fourier transform on said model of observed signal{circumflex over (X)}(m), providing a time domain model {tilde over(S)}(n) of said observed signal {circumflex over (X)}(m), and an inversediscrete Fourier transform of said frequency domain channel estimate{tilde over (H)}(m) providing a time domain channel estimate {tilde over(G)}(p) with length P wherein p=0, 1, . . . , P−1, whitening said timedomain model {tilde over (S)}(n) of said observed signal {circumflexover (X)}(m), providing a whitened time domain model Ŝ(n) of said timedomain model {tilde over (S)}(n) and a whitened time domain channelestimate Ĝ(p) for p=0, 1, . . . , P−1, and jointly detecting saidreceived at least two communication signals by performing soft valuecalculations based on maximum likelihood detection of said whitened timedomain model Ŝ(n), using said whitened time domain channel estimate Ĝ(p)for p=0, 1, . . . , P−1, whereby said at least two receivedcommunication signals are decoded.
 13. The receiver as claimed in claim12, wherein said means comprises Application Specific IntegratedCircuits (ASICs) or a computer program comprising stored programinstructions to be executed by a microprocessor or a digital signalprocessor.